Intellectual Merit: There is compelling evidence that the distinct stages of sleep play an essential role in the long-term consolidation of memories (Marshall & Born 2007). Specifically, slow-wave sleep (SWS), which is hallmarked by slow oscillatory activity (< 1 Hz) in the human electro-encephalogram (EEG), has been implicated in memory consolidation. We demonstrated that weak electric currents (<1mA, <1Hz and DC) applied to the scalp during SWS modulate these endogenous EEG rhythms and can improve human memory performance (Marshall 2006a). Moreover, application of the same weak currents during learning modulates ongoing EEG rhythms that are typical for the awake state in humans and boosts immediate performance in some learning tasks (Kirov 2009). Yet, despite these remarkable phenomenological findings, the question of how weak currents can modulate brain oscillations and induce plastic changes in brain function remains fundamentally unaddressed. Here we propose to quantitatively address this question through the development of computational models that are tightly constrained by specialized brain-slice experiments and validated through targeted human subject experiments. A central question is: how can weak electric currents, that appear insufficient to modulate excitability or plasticity in quiescent neurons, exert such a powerful effect on oscillations and learning? Our central hypothesis is that weak currents couple into ongoing slow oscillatory activity that then boost their modulatory effect on synaptic plasticity. Preliminary data from our group and others already provides strong evidence for modulation of endogenous rhythmic network activity by applied currents - at intensities considered too weak to affect single neuron function. Concurrently, we and other groups have investigated links between slow wave activity and memory consolidation, including by application of weak currents in human. But a specific connection between the effects of applied weak currents on slow-wave rhythms and plasticity has so far not been explored. Guided by computational models, the crucial empirical link between the two will be sought by probing lasting changes resulting from weak-current stimulation of an in vitro cortical preparation that exhibits SWA. Targeted human experiments will directly test if applied currents also enhance the consolidation of other SWS-mediated learning as the hypothesis would suggest, or rather, if the effect is limited to hippocampus-related learning, thus providing significant constraints to the computational models. Broader Impacts: Weak applied currents are being explored in a number of empirical studies for their potential benefits to treat depression and neuropathic pain, to assist motor learning after stroke, or more generally, to enhance cognitive performance and to improve learning. The promise of this technique is that weak currents can be applied non-invasively with a potentially broad range of applications and minimal side effects. The enigma in this potentially transformative clinical tool, however, is that the electric field strengths generated by these currents in most studies are two orders of magnitude below what is required to activate an otherwise silent neuron. Currently, research in this area is almost entirely phenomenological and the few mechanistic explanations for the promising phenomenological observations are superficial (e.g. describing all brain function as a sliding scale of excitability) and do not address plasticity - as such, there is no rational basis for improving and targeting stimulation protocols. This work is the first attempt at establishing the mechanistic link between applied currents on endogenous rhythms and the associated SWS-related learning enhancements. Evidently, such an analysis will address basic science questions about the link between endogenous SWS and learning, add to the set of experimental tools which can be used to study cognition, and, shed light on the functional and causal role of the ubiquitous endogenous rhythms generated by the brain. Consistent with present call for US/German Collaborative Research in Computational Neuroscience this project will combined the expertise of international researchers in the areas of: (1) effects of noninvasive electrical stimulation on nervous tissue (Bikson, US), EEG signal analysis and computational network models (Parra, US), human sleep and learning with applied currents (Marshall, Germany), and dynamical systems and machine learning (Claussen/Martinetz, Germany; Parra, US).